If f(x)=sin x,x in` [-pi//2,pi//2]` then which one of the following is not correct ?

Options

A. f(x) is increasing on the `[-pi //2 ,pi//2]`
B. fof (x) is increasing on `[-pi//2,pi//2]`
C. fof (x) is increasing on `[-pi//2,pi//2]`
D. fof (x) is decreasing on `[-pi//2,0]` and is increasing on` [-pi//2 ,pi //2]`

Answer

A

Explanation

We know that sin x is that sin x is increasing on `[-pi//2, pi//2]`
f(x) sinx
`rArr fof (x) sin (sin x)`
`rArr d/dx " {fof (x) =sin (sin x) cos " x ge 0 "for" x in [-pi //2 ,pi//2]`
Now
f(x)= sin x
`rArr fof (x) = sin (Sin x) `
`rArr "fof (x) is increasing on" [-pi//2,pi//2]`
since fof (x) =sin 1 fof `f(-pi/2)`= sin 1
Now these values are not attained at any ohter point Hence fof is invertible on `[-pi//2 pi//2]`